I want to calculate the ' great circle distance' between two points on the surface of an ellipsoid. Though because of the extra radius, the great circle distance is not what I am looking for. Also I have not a center of the ellipsoid on [0,0,0], which makes the calculation more difficult, besides this I only have the cartesian coordinates of the two points and the center.

"Els " <y.e.t.reeuwijk@student.utwente.nl> wrote in message <hseek4$50$1@fred.mathworks.com>...
> Dear all,
> I want to calculate the ' great circle distance' between two points on the surface of an ellipsoid. Though because of the extra radius, the great circle distance is not what I am looking for.
> ......

I presume that when you say "great circle distance" you mean the distance along the geodesic path on the ellipsoidal surface between the two points. This is a problem in the calculus of variations which would require some considerable effort to solve. There is a discussion of this topic on the two Mathworld websites

"Els " <y.e.t.reeuwijk@student.utwente.nl> wrote in message <hseek4$50$1@fred.mathworks.com>...
> Dear all,
>
> I want to calculate the ' great circle distance' between two points on the surface of an ellipsoid. Though because of the extra radius, the great circle distance is not what I am looking for. Also I have not a center of the ellipsoid on [0,0,0], which makes the calculation more difficult, besides this I only have the cartesian coordinates of the two points and the center.
>
> This is what I have now, anyone knows how to calculate this distance?
>
Great circle distances for spheres and various ellipsoids can be calculated with the Mapping Toolbox, if you have it.

Mark, thanks a lot. I found the Vincenty formula on wikipedia as well, but thought that I was only applicable on large ellipsoids (earth).

I corrigated my cartesian coordinates, so that my center was 0,0,0. And then I transformed my cartesian coordinates to geodetic latitude and latitude. And finally I implemented the formula of Vincenty and got the distances I was looking for.

BUT...now I want to plot this distance between these two points on my ellipsoid as well. How do I do this?

Subject:Distance between two points on the surface of a ellipsoidFrom:Crigou

"Els" wrote in message <hsi815$35$1@fred.mathworks.com>...
> Mark, thanks a lot. I found the Vincenty formula on wikipedia as well, but thought that I was only applicable on large ellipsoids (earth).
>
> I corrigated my cartesian coordinates, so that my center was 0,0,0. And then I transformed my cartesian coordinates to geodetic latitude and latitude. And finally I implemented the formula of Vincenty and got the distances I was looking for.
>
> BUT...now I want to plot this distance between these two points on my ellipsoid as well. How do I do this?

*****************************

Hi Els,

It is not my intention to disappoint you about the Vincenty's formula, but please note the following:

The famous NGS Online Inverse Geodesic Calculator (basing on Vincenty's formulae) is the conventional reference means to calculate the distance between any two locations on the earth ellipsoid:

But above calculator is still problematic. Especially between two near-antipodal locations, the computed distance can show an error of some tens of kilometres !!! The origin of the numeric trouble was identified long time ago by Thaddeus Vincenty (page 92):

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